Green Paging and Parallel Paging

We study two fundamental variants of the classic paging problem: green paging and parallel paging. In green paging one can choose the exact memory capacity in use at any given instant, between a maximum of k and a minimum of k/p pages; the goal is to minimize the integral of this number over the time required to complete a computation (note that running at lower capacity is not necessarily better, since might disproportionately increase the total completion time). In parallel paging, a memory of k pages is shared between p processors, each carrying out a separate computation; the goal is to minimize the respective completion times. We show how these two different problems are strictly related: any efficient solution to green paging can be converted into an efficient solution to parallel paging, and any lower bound for green paging can be converted into a lower bound for parallel paging---in both cases in a black-box fashion. Exploiting this relation, we provide tight upper and lower bounds of Θ(log p) on the competitive ratio with O(1) resource augmentation for both problems.